Exact Solutions for Equations of Bose-Fermi Mixtures in One-Dimensional Optical Lattice

We present two new families of stationary solutions for equations of Bose-Fermi mixtures with an elliptic function potential with modulus k. We also discuss particular cases when the quasiperiodic solutions become periodic ones. In the limit of a sinusoidal potential (k ? 0) our solutions model a qu...

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Bibliographic Details
Published in:Symmetry, integrability and geometry, methods and applications integrability and geometry, methods and applications, 2007-01, Vol.3, p.071
Main Author: Kostov, Nikolay A.
Format: Article
Language:English
Subjects:
Bose-Fermi mixtures
one dimensional optical lattice
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Summary:We present two new families of stationary solutions for equations of Bose-Fermi mixtures with an elliptic function potential with modulus k. We also discuss particular cases when the quasiperiodic solutions become periodic ones. In the limit of a sinusoidal potential (k ? 0) our solutions model a quasi-one dimensional quantum degenerate Bose-Fermi mixture trapped in optical lattice. In the limit k ? 1 the solutions are expressed by hyperbolic function solutions (vector solitons). Thus we are able to obtain in an unified way quasi-periodic and periodic waves, and solitons. The precise conditions for existence of every class of solutions are derived. There are indications that such waves and localized objects may be observed in experiments with cold quantum degenerate gases.
ISSN:1815-0659
1815-0659
DOI:10.3842/SIGMA.2007.071